let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being good InitHalting Program of SCM+FSA
for a being read-write Int-Location st s . (intloc 0) = 1 & s . a <= 0 holds
DataPart (IExec ((Times (a,I)),p,s)) = DataPart s
let s be State of SCM+FSA; :: thesis: for I being good InitHalting Program of SCM+FSA
for a being read-write Int-Location st s . (intloc 0) = 1 & s . a <= 0 holds
DataPart (IExec ((Times (a,I)),p,s)) = DataPart s
let I be good InitHalting Program of SCM+FSA; :: thesis: for a being read-write Int-Location st s . (intloc 0) = 1 & s . a <= 0 holds
DataPart (IExec ((Times (a,I)),p,s)) = DataPart s
let a be read-write Int-Location ; :: thesis: ( s . (intloc 0) = 1 & s . a <= 0 implies DataPart (IExec ((Times (a,I)),p,s)) = DataPart s )
assume A1: s . (intloc 0) = 1 ; :: thesis: ( not s . a <= 0 or DataPart (IExec ((Times (a,I)),p,s)) = DataPart s )
set s0 = Initialized s;
set p0 = p;
A2: ( Stop SCM+FSA is_closed_on Initialized s,p & Stop SCM+FSA is_halting_on Initialized s,p ) by SCMFSA7B:18, SCMFSA7B:19;
A3: ( ( for a being read-write Int-Location holds (Initialized s) . a = s . a ) & ( for f being FinSeq-Location holds (Initialized s) . f = s . f ) ) by SCMFSA6C:3;
A4: (Initialized s) . (intloc 0) = 1 by SCMFSA6A:38;
assume s . a <= 0 ; :: thesis: DataPart (IExec ((Times (a,I)),p,s)) = DataPart s
then A5: (Initialized s) . a <= 0 by SCMFSA6C:3;
A6: IExec (((Stop SCM+FSA) ';' (Stop SCM+FSA)),p,(Initialized s)) = IncIC ((IExec ((Stop SCM+FSA),p,(IExec ((Stop SCM+FSA),p,(Initialized s))))),(card (Stop SCM+FSA))) by SCMFSA6B:20;
A7: DataPart (IExec ((Stop SCM+FSA),p,(Initialized s))) = DataPart (Initialized (Initialized s)) by SCMFSA8C:14
.= DataPart (Initialized s) ;
A8: ( Stop SCM+FSA is_closed_on Initialized s,p & Stop SCM+FSA is_halting_on Initialized s,p ) by SCMFSA7B:18, SCMFSA7B:19;
then ( Times (a,I) is_closed_on Initialized s,p & Times (a,I) is_halting_on Initialized s,p ) by A5, SCMFSA8B:21;
then DataPart (IExec ((Times (a,I)),p,s)) = DataPart (IExec ((Times (a,I)),p,(Initialized s))) by A4, A3, SCMFSA8C:19
.= DataPart (IExec (((Stop SCM+FSA) ';' (Stop SCM+FSA)),p,(Initialized s))) by A5, A2, A4, SCMFSA8A:23, SCMFSA8C:44 ;
hence DataPart (IExec ((Times (a,I)),p,s)) = DataPart (IExec ((Stop SCM+FSA),p,(IExec ((Stop SCM+FSA),p,(Initialized s))))) by A6, MEMSTR_0:79
.= DataPart (IExec ((Stop SCM+FSA),p,(Initialized s))) by A8, A4, A7, SCMFSA8C:20
.= DataPart s by A1, A7, SCMFSA8C:7 ;
:: thesis: verum